Analytical estimations of limit cycle amplitude for delay-differential equations

Molnár Tamás G. and Insperger Tamás and Stépán Gábor: Analytical estimations of limit cycle amplitude for delay-differential equations. (2016)

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The amplitude of limit cycles arising from Hopf bifurcation is estimated for nonlinear delay-differential equations by means of analytical formulas. An improved analytical estimation is introduced, which allows more accurate quantitative prediction of periodic solutions than the standard approach that formulates the amplitude as a square-root function of the bifurcation parameter. The improved estimation is based on special global properties of the system: the method can be applied if the limit cycle blows up and disappears at a certain value of the bifurcation parameter. As an illustrative example, the improved analytical formula is applied to the problem of stick balancing.

Item Type: Journal
Other title: Honoring the career of Tibor Krisztin on the occasion of his sixtieth birthday
Publication full: Electronic journal of qualitative theory of differential equations : special edition
Date: 2016
Volume: 2
Number: 77
ISSN: 1417-3875
Number of Pages: 10
Language: English
DOI: 10.14232/ejqtde.2016.1.77
Uncontrolled Keywords: Differenciálegyenlet - késleltetett, Bifurkáció
Additional Information: Bibliogr.: p. 8-10. ; összefoglalás angol nyelven
Date Deposited: 2021. Nov. 11. 14:20
Last Modified: 2021. Nov. 12. 09:42

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